Problem: Simplify the following expression: $y = \dfrac{-72p^2 - 80p}{48p^2 - 56p}$ You can assume $p \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-72p^2 - 80p = - (2\cdot2\cdot2\cdot3\cdot3 \cdot p \cdot p) - (2\cdot2\cdot2\cdot2\cdot5 \cdot p)$ The denominator can be factored: $48p^2 - 56p = (2\cdot2\cdot2\cdot2\cdot3 \cdot p \cdot p) - (2\cdot2\cdot2\cdot7 \cdot p)$ The greatest common factor of all the terms is $8p$ Factoring out $8p$ gives us: $y = \dfrac{(8p)(-9p - 10)}{(8p)(6p - 7)}$ Dividing both the numerator and denominator by $8p$ gives: $y = \dfrac{-9p - 10}{6p - 7}$